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We study a quantum phase transition in a system of dipoles confined in astack of $N$ identical one-dimensional lattices (tubes) polarizedperpendicularly to the lattices. In this arrangement the intra-latticeinteraction is purely repulsive preventing the system collapse and theinter-lattice one is attractive. The dipoles may represent polar molecules orindirect excitons. The transition separates two phases; in one of themsuperfluidity (understood as algebraic decay of the corresponding correlationfunctions) takes place in each individual lattice, in the other (chainsuperfluid) the order parameter is the product of bosonic operators from alllattices. We argue that in the presence of finite inter-lattice tunneling thetransition belongs to the universality class of the $q=N$ two-dimensionalclassical Potts model. For $N=2,3,4$ the corresponding low energy field theoryis the model of Z$_N$ parafermions perturbed by the thermal operator. Resultsof Monte Carlo simulations are consistent with these predictions. The detectionscheme for the chain superfluid of indirect excitons is outlined.

Parafermion excitations in superfluid of quasi-molecular chains